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Compute statistics and regression in one pass

Project description

RunStats is an Apache2 licensed Python module for online statistics and online regression. Statistics and regression summaries are computed in a single pass. Previous values are not recorded in summaries.

Long running systems often generate numbers summarizing performance. It could be the latency of a response or the time between requests. It’s often useful to use these numbers in summary statistics like the arithmetic mean, minimum, standard deviation, etc. When many values are generated, computing these summaries can be computationally intensive. It may even be infeasible to keep every recorded value. In such cases computing online statistics and online regression is necessary.

In other cases, you may only have one opportunity to observe all the recorded values. Python’s generators work exactly this way. Traditional methods for calculating the variance and other higher moments requires multiple passes over the data. With generators, this is not possible and so computing statistics in a single pass is necessary.

There are also scenarios where a user is not interested in a complete summary of the entire stream of data but rather wants to observe the current state of the system based on the recent past. In these cases exponential statistics are used. Instead of weighting all values uniformly in the statistics computation, an exponential decay weight is applied to older values. The decay rate is configurable and provides a mechanism for balancing recent values with past values.

The Python RunStats module was designed for these cases by providing classes for computing online summary statistics and online linear regression in a single pass. Summary objects work on sequences which may be larger than memory or disk space permit. They may also be efficiently combined together to create aggregate summaries.

Features

  • Pure-Python
  • Fully Documented
  • 100% Test Coverage
  • Numerically Stable
  • Optional Cython-optimized Extension (5-100 times faster)
  • Statistics summary computes mean, variance, standard deviation, skewness, kurtosis, minimum and maximum.
  • Regression summary computes slope, intercept and correlation.
  • Developed on Python 3.9
  • Tested on CPython 3.6, 3.7, 3.8, 3.9
  • Tested on Linux, Mac OS X, and Windows
  • Tested using GitHub Actions
https://github.com/grantjenks/python-runstats/workflows/integration/badge.svg

Quickstart

Installing RunStats is simple with pip:

$ pip install runstats

You can access documentation in the interpreter with Python’s built-in help function:

>>> import runstats
>>> help(runstats)                             # doctest: +SKIP
>>> help(runstats.Statistics)                  # doctest: +SKIP
>>> help(runstats.Regression)                  # doctest: +SKIP
>>> help(runstats.ExponentialStatistics)       # doctest: +SKIP

Tutorial

The Python RunStats module provides three types for computing running statistics: Statistics, ExponentialStatistics and Regression.The Regression object leverages Statistics internally for its calculations. Each can be initialized without arguments:

>>> from runstats import Statistics, Regression, ExponentialStatistics
>>> stats = Statistics()
>>> regr = Regression()
>>> exp_stats = ExponentialStatistics()

Statistics objects support four methods for modification. Use push to add values to the summary, clear to reset the summary, sum to combine Statistics summaries and multiply to weight summary Statistics by a scalar.

>>> for num in range(10):
...     stats.push(float(num))
>>> stats.mean()
4.5
>>> stats.maximum()
9.0
>>> stats += stats
>>> stats.mean()
4.5
>>> stats.variance()
8.68421052631579
>>> len(stats)
20
>>> stats *= 2
>>> len(stats)
40
>>> stats.clear()
>>> len(stats)
0
>>> stats.minimum()
nan

Use the Python built-in len for the number of pushed values. Unfortunately the Python min and max built-ins may not be used for the minimum and maximum as sequences are expected instead. Therefore, there are minimum and maximum methods provided for that purpose:

>>> import random
>>> random.seed(0)
>>> for __ in range(1000):
...     stats.push(random.random())
>>> len(stats)
1000
>>> min(stats)
Traceback (most recent call last):
    ...
TypeError: ...
>>> stats.minimum()
0.00024069652516689466
>>> stats.maximum()
0.9996851255769114

Statistics summaries provide five measures of a series: mean, variance, standard deviation, skewness and kurtosis:

>>> stats = Statistics([1, 2, 5, 12, 5, 2, 1])
>>> stats.mean()
4.0
>>> stats.variance()
15.33333333333333
>>> stats.stddev()
3.915780041490243
>>> stats.skewness()
1.33122127314735
>>> stats.kurtosis()
0.5496219281663506

All internal calculations use Python’s float type.

Like Statistics, the Regression type supports some methods for modification: push, clear and sum:

>>> regr.clear()
>>> len(regr)
0
>>> for num in range(10):
...     regr.push(num, num + 5)
>>> len(regr)
10
>>> regr.slope()
1.0
>>> more = Regression((num, num + 5) for num in range(10, 20))
>>> total = regr + more
>>> len(total)
20
>>> total.slope()
1.0
>>> total.intercept()
5.0
>>> total.correlation()
1.0

Regression summaries provide three measures of a series of pairs: slope, intercept and correlation. Note that, as a regression, the points need not exactly lie on a line:

>>> regr = Regression([(1.2, 1.9), (3, 5.1), (4.9, 8.1), (7, 11)])
>>> regr.slope()
1.5668320150154176
>>> regr.intercept()
0.21850113956294415
>>> regr.correlation()
0.9983810791694997

Both constructors accept an optional iterable that is consumed and pushed into the summary. Note that you may pass a generator as an iterable and the generator will be entirely consumed.

The ExponentialStatistics are constructed by providing a decay rate, initial mean, and initial variance. The decay rate has default 0.9 and must be between 0 and 1. The initial mean and variance default to zero.

>>> exp_stats = ExponentialStatistics()
>>> exp_stats.decay
0.9
>>> exp_stats.mean()
0.0
>>> exp_stats.variance()
0.0

The decay rate is the weight by which the current statistics are discounted by. Consequently, (1 - decay) is the weight of the new value. Like the Statistics class, there are four methods for modification: push, clear, sum and multiply.

>>> for num in range(10):
...     exp_stats.push(num)
>>> exp_stats.mean()
3.486784400999999
>>> exp_stats.variance()
11.593430921943071
>>> exp_stats.stddev()
3.4049127627507683

The decay of the exponential statistics can also be changed. The value must be between 0 and 1.

>>> exp_stats.decay
0.9
>>> exp_stats.decay = 0.5
>>> exp_stats.decay
0.5
>>> exp_stats.decay = 10
Traceback (most recent call last):
  ...
ValueError: decay must be between 0 and 1

The clear method allows to optionally set a new mean, new variance and new decay. If none are provided mean and variance reset to zero, while the decay is not changed.

>>> exp_stats.clear()
>>> exp_stats.decay
0.5
>>> exp_stats.mean()
0.0
>>> exp_stats.variance()
0.0

Combining ExponentialStatistics is done by adding them together. The mean and variance are simply added to create a new object. To weight each ExponentialStatistics, multiply them by a constant factor. If two ExponentialStatistics are added then the leftmost decay is used for the new object. The len method is not supported.

>>> alpha_stats = ExponentialStatistics(iterable=range(10))
>>> beta_stats = ExponentialStatistics(decay=0.1)
>>> for num in range(10):
...     beta_stats.push(num)
>>> exp_stats = beta_stats * 0.5 + alpha_stats * 0.5
>>> exp_stats.decay
0.1
>>> exp_stats.mean()
6.187836645

All internal calculations of the Statistics and Regression classes are based entirely on the C++ code by John Cook as posted in a couple of articles:

The ExponentialStatistics implementation is based on:

  • Finch, 2009, Incremental Calculation of Weighted Mean and Variance

The pure-Python version of RunStats is directly available if preferred.

>>> import runstats.core   # Pure-Python
>>> runstats.core.Statistics
<class 'runstats.core.Statistics'>

When importing from runstats the Cython-optimized version _core is preferred and the core version is used as fallback. Micro-benchmarking Statistics and Regression by calling push repeatedly shows the Cython-optimized extension as 20-40 times faster than the pure-Python extension.

License

Copyright 2013-2021 Grant Jenks

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

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